where \(T\)  is the exposure time, \(E_R\)  is the reconstructed energy, \(E\) 
is the true gamma-ray energy, and \(P(E_R|E)\)  is the energy dispersion
function that takes the finite energy resolution of the detector into
account. For the detector specification of the CTA North such as the
effective area \(A_{\rm eff}(E_R)\) , we adopt information extracted from
www.cta-observatory.org, and for the exposure time, we assume
500 hours [1]}, [2]}. For the energy resolution
we adopt a flat value of 10%, i.e., \(\Delta E/ E = 0.1\) . The photon
counts in this given energy bin and spatial pixel are then added on
top of other background events caused by both the cosmic ray electrons
and protons, for which we adopt a model given by
Ref. [3]}. Then we perform a Poisson likelihood
analysis by combining the information on all the pixels in both the
spatial and energy bins under the null hypothesis that there is no DM
component in the mock data, and obtain the expected upper limits on
the annihilation cross section at 95% confidence level (CL).
<FIGURE><FIGURE><FIGURE><FIGURE>